Question

Two balls are projected simultaneously with the same velocity u from the top of a tower, one vertically upwards and the other vertically downwards. Their respective times of the journeys are $t_1 $ and $ t_2$ . At the time of reaching the ground, the ratio of their final velocities is

• A. 1:1
• B. 1:2
• C. 2:3
• D. 2:1

Answer 1

Answer: (A)

Using: $v ^{2}= u ^{2}+2 aS$
where, v final velocity, u initial velocity a is acceleration and S is displacement of the particle.
For particle $1: v _{1}^{2}= u _{1}^{2}+2(- g )(- h )$ taking upward direction positive
For particle $2: v _{2}^{2}= u _{2}^{2}+2(- g )(- h )$
as $u_{1}=u_{2}$ and displacement of both the particle is equal to height of tower, their velocities at time of reaching ground will be equal.